One shopper waiting in the queue said: "Costco can't get a break can it?"
The Herald has approached Costco for a statement on this morning's incident.
The system failure came just a day after hundreds were evacuated from the new mega retail store when smoke from a commercial oven activated the alarms.
A Costco customer told the Herald: "I just entered the store 10 minutes before and we're in the second aisle when the sirens went off and we were asked to leave our trolleys and to evacuate.
"It was absolute chaos to get the people out and like a stampede to get back in ... People were crowding around the door to get back in but staff ushered people to get across the road," they said.
Costco encountered its first problem last week on their second day of opening when the store plunged into darkness after an in-store power cut.
Pictures posted to social media showed people in the food court continuing to eat despite the blackout.